Unfolding the Earth

Mapping the earth is a classic problem. For thousands of years cartographers, mathematicians, and inventors have come up with methods to map the curved surface of the earth to a flat plane. The main problem is that you cannot do this perfectly, such that both the shape and size of the surface are depicted properly everywhere. This has intrigued me for a long time. Why not just take a map of a small part of the earth, which is almost perfect, glue neighboring maps to it, and repeat this until the whole earth is shown? Of course you get interrupts, but does this matter? What does such a map look like? To check this out, we developed myriahedral projections.